1. Field of the Invention
The present invention relates generally to determining geological properties of subsurface formations using Nuclear Magnetic Resonance (“NMR”) methods for logging wellbores, particularly for correcting for the effects of tool motion and pulse sequence timing on NMR signals.
2. Description of the Related Art
A variety of techniques are currently utilized in determining the presence and estimation of quantities of hydrocarbons (oil and gas) in earth formations. These methods are designed to determine formation parameters, including among other things, the resistivity, porosity and permeability of the rock formation surrounding the wellbore drilled for recovering the hydrocarbons. Typically, the tools designed to provide the desired information are used to log the wellbore. Much of the logging is done after the well bores have been drilled. More recently, wellbores have been logged while drilling, which is referred to as measurement-while-drilling (MWD) or logging-while-drilling (LWD).
One commonly used technique involves utilizing Nuclear Magnetic Resonance (NMR) logging tools and methods for determining, among other things, porosity, hydrocarbon saturation and permeability of the rock formations. The NMR logging tools are utilized to excite the nuclei of the liquids in the geological formations surrounding the wellbore so that certain parameters such as nuclear spin density, longitudinal relaxation time (generally referred to in the art as T1) and transverse relaxation time (generally referred to as T2) of the geological formations can be measured. From such measurements, porosity, permeability and hydrocarbon saturation are determined, which provides valuable information about the make-up of the geological formations and the amount of extractable hydrocarbons.
The NMR tools generate a static magnetic field in a region of interest surrounding the wellbore. NMR is based on the fact that the nuclei of many elements have angular momentum (spin) and a magnetic moment. The nuclei have a characteristic Larmor resonant frequency related to the magnitude of the magnetic field in their locality. Over time the nuclear spins align themselves along an externally applied static magnetic field creating a net magnetization. This equilibrium situation can be disturbed by a pulse of an oscillating magnetic field, which tips the spins with resonant frequency within the bandwidth of the oscillating magnetic field away from the static field direction. The angle θ through which the spins exactly on resonance are tipped is given by the equation:θ=γB1tp/2  (1)where γ is the gyromagnetic ratio, B1, is the magnetic flux density amplitude of the sinusoidally oscillating field and tp is the duration of the RF pulse.
After tipping, the spins precess around the static field at a particular frequency known as the Larmor frequency ω0 given byω0=γB0  (2)where B0 is the static magnetic flux density. For hydrogen nuclei γ/2π=4258 Hz/Gauss, so that a static field of 235 Gauss, would produce a precession frequency of 1 MHz. At the same time, the magnetization returns to the equilibrium direction (i.e., aligned with the static field) according to a decay time known as the “spin-lattice relaxation time” or T1. T1 is controlled by the molecular environment and is typically ten to one thousand milliseconds in rocks.
At the end of a θ=90° tipping pulse, spins on resonance are pointed in a common direction perpendicular to the static field, and they precess at the Larmor frequency. However, because of inhomogeneity in the static field due to the constraints on tool shape, imperfect instrumentation, or microscopic material heterogeneities, each nuclear spin precesses at a slightly different rate. Hence, after a time long compared to the precession period, but shorter than T1, the spins will no longer be precessing in phase. This de-phasing occurs with a time constant that is commonly referred to as T2*. Dephasing due to static field inhomogeneity can be recovered by generating spin echoes (see below). The remaining dephasing is characterized by the time constant T2 and is due to properties of the material.
A receiving coil is designed so that a voltage is induced by the precessing spins. Only that component of the nuclear magnetization that is precessing in the plane perpendicular to the static field is sensed by the coil. After a 180° tipping pulse (an “inversion pulse”, the spins on resonance are aligned opposite to the static field and the magnetization relaxes along the static field axis to the equilibrium direction. Hence, a signal will be generated after a 90° tipping pulse, but not after a 180° tipping pulse in a generally uniform magnetic field.
While many different methods for measuring T1 have been developed, a single standard known as the CPMG sequence (Carr-Purcell-Meiboom-Gill) for measuring T2 has evolved. In contrast to laboratory NMR magnets, well logging tools have inhomogeneous magnetic fields due to the constraints on placing the magnets within a tubular tool and the inherent “inside-out” geometry. Maxwell's divergence theorem dictates that there cannot be an extended region of high homogeneity outside the tool. Therefore in typical well bores, T2*<<T2, and the free induction decay becomes a measurement of the apparatus-induced inhomogeneities. To measure the true T2 in such situations, it is necessary to cancel the effect of the apparatus-induced inhomogeneities. To accomplish the same, a series of pulses is applied to repeatedly refocus the spin system, canceling the T2* effects and forming a series of spin echoes. The decay of echo amplitude is a true measure of the decay due to material properties. Furthermore it can be shown that the decay is in fact composed of a number of different decay components forming a T2 distribution. The echo decay data can be processed to reveal this distribution which is related to rock pore size distribution and other parameters of interest to the well log analyst.
Tool motion can seriously affect the performance of NMR tools used in an MWD environment. NMR tools that have static magnetic fields with complete rotational symmetry are unaffected by rotation of the tool since the fields in the region of examination do not change during the measurement sequence. However, any axial or transverse (orthogonal to the tool axis) component of tool motion will affect the NMR signal.
There are many well-known artifacts of motion that show up in signals in downhole logging. These artifacts are theoretically expected and are attributable to such factors as rotation, transverse vibration and axial motion. In addition to these motion artifacts the NMR signal amplitude can be reduced due to insufficient wait time for polarization after the end of an echo sequence.
Artifacts of rotation are a result of the typical stationary B0 field of the system not being completely axisymmetric. Rotation of the drillstring therefore causes (periodic) NMR signal losses during a spin echo train. Artifacts from transverse vibrations generally occur because of drilling or because of mud circulation through a mud motor. The obtained vibration frequency spectrum usually includes some dominant frequencies that are directly related to the rotational speed of the motor or drill string.
Axial motion of the drill string gives rise to two distinct artifacts. A first artifact of axial motion is caused by the motion of the drillstring through the borehole. The rate of penetration (ROP) of the drill string can be recorded electronically and later retrieved from a computer file. Obviously, the ROP at the drill bit differs slightly from the electronically-recorded value of the ROP which is measured at the surface. This discrepancy between ROP values is due to limited time resolution of the computer file as well as to flexibility of the drill string. A second artifact of axial motion exhibits itself as higher frequency axial vibrations. These vibrations can be measured with an accelerometer in the NMR tool.
Application of an insufficient wait time between consecutive pulse sequences can give rise to yet another artifact. Typically, after the end of an echo sequence obtained with axial motion of the drill string, the z-magnetization is substantially zero. This z-magnetization is generally non-zero when no such motion exists. A wait time is generally applied after an echo sequence to allow the protons to re-align along the direction of the static magnetic field. This re-magnetization occurs with a characteristic relaxation time known as the spin-lattice relaxation time T1. Usually, there exists a distribution of T1 times similar to the well-known T2 distribution.
U.S. Pat. No. 5,389,877 issued to Sezginer describes a truncated CPMG sequence in which the sequence duration and recovery delay are so short that only signals from the clay and capillary bound fluids are detected. A truncated sequence has the advantage that the effect of tool motion on the measurements is reduced due to the short measurement time (approx. 50 ms, compared to greater than 300 ms for normal downhole CPMG measurements.) As discussed in U.S. Pat. No. 5,705,927 issued to Kleinberg, resonance regions of many prior art instruments are of the order of 1 mm. Accordingly, a lateral vibration at a frequency of 50 Hz having an amplitude of 1 mm (10 g acceleration) would disable the instrument. The Kleinberg '927 patent discloses making the length of each CPMG sequence small, e.g. 10 ms, so that the drill collar cannot be displaced by a significant fraction of the vertical or radial extent of the sensitive region during a CPMG pulse sequence. However, as noted above, using such short sequences and short wait times only gives an indication of the bound fluid volume and gives no indication of the total fluid volume.
U.S. Pat. No. 6,268,726 to Prammer et al., teaches the use of motion sensors on an MWD apparatus that makes measurements of tool motion of a NMR sensor assembly. Measurements are made by the NMR sensor during continued drilling operations, and subsequently, the measurements made by the motion sensor are used to select a subset of the NMR measurements that meet certain requirements on tool motion and hence would be expected to give a reasonable insensitivity to tool motion. U.S. Pat. No. 6,459,263 to Hawkes et al, having the same assignee as the present application and the contents of which are fully incorporated herein by reference, uses the output of motion sensors in combination with predictive filtering to control the timing of pulses for a modified (as in the Hawkes '013 patent) or conventional CPMG sequence.
U.S. Pat. No. 6,566,874 to Speier et al. teaches several approaches to dealing with problems associated with tool motion. In one embodiment, measurements are made of two different echo trains that have different sensitivities to tool motion. A tool is used having two different regions of examination: a high gradient zone defined by one set of magnets and antennas, and a low gradient zone defined by another set of magnets and antennas. The effect of tool motion on the signal amplitude is greater in the high gradient zone than in the low gradient zone. Using these two sets of signals and knowing the gradients of the respective zones, it is possible to estimate what the signal would have been without the tool motion. The Speier '874 patent also teaches that sensitivity to motion may be varied by different field geometries with different gradients. This requirement of having two different regions of examination complicates the hardware. Another drawback (noted in Speier '874) to the above-described techniques is that the measurements must be separated in time and/or space. In order to interpret the results it is assumed that, in the absence of motion, the NMR signal (and therefore the formation measured) is the same in both measurements. For a continuously moving logging tool, this condition is not always given. Also the motion during the two measurements should be the same, or at least have the same characteristics.
In another embodiment taught by Speier '874, measurements are processed to obtain both the T1 and T2 distribution. The effect of tool motion is different on the two types of measurements. This approach has at least two drawbacks. The first is that T1 determination is time consuming. A second drawback is that in the absence of an exact knowledge of the ratio of T1/T2, the method can only be used for quality control and not for determining both the T1 and T2 distributions.
U.S. patent application Ser. No. 10/918,965 of Blanz et al. discloses a method of processing and an apparatus used for processing Nuclear Magnetic Resonance (NMR) signals from an earth formation. The spin echo signals are corrected using a function of the velocity to give corrected spin echo signals. The correction may be implemented by scaling the spin echo signals by a normalizing function related to the axial velocity and a reference velocity. The correction factor may be applied to the in-phase component, quadrature component or to the amplitude of the spin echo signals of a spin echo sequence. The invention of Blanz uses measurements or estimates of the axial velocity in applying the correction. Such measurements or estimates of the downhole axial velocity may be difficult to obtain. There is a need for computational methods to reduce the effects of motion artifacts encountered in MWD testing without using the downhole axial velocity